# Homework Help: Expection of Angular Momentum

1. Nov 11, 2009

### wam_mi

1. The problem statement, all variables and given/known data

I am trying to calculate the expectation of the y-component of the angular momentum L.
$<L_{y}>$. How should I approach this?

2. Relevant equations

I try to write it in terms of the following commutator

$L(y) = \frac{2*pi}{ih} [L_{x}, L_{z}]$

3. The attempt at a solution

2. Nov 11, 2009

### Avodyne

What do you know about the state in which you are to take the expectation value?

3. Nov 11, 2009

### wam_mi

Hi there, the state is given as |l, m>, where l is the orbital angular momentum quantum number, and m is the magnetic moment quantum number.

I want to prove that to compute <l,m| L(y) |l,m> = <L(y)> =0, how should I approach this?

Many thanks!

4. Nov 11, 2009

### gabbagabbahey

If I were you, I'd write $L_y$ in terms of the raising and lowering operators $L_{\pm}$...

5. Nov 11, 2009